In working on Giordano Bruno's "geometric rhetoric" (that is, the geometricmetaphors in his philosophical treatises and works of literature) I have comeacross the term "mathesis" many times. Although the etymology of this wordrefers simply to "knowledge" or "an act of learning," I am curious if in thesixteenth century it was used more commonly to mean arithmetic and geometry.Bruno seems to use it in this way. In the _Eroici furori_ he speaks ofArchimedes's "mathesis," for example, and he calls his own revision of geometrya "mathesis" (see his _Articuli centum et sexaginta adversus huius tempestatismathematicos atque philosophos_. Prague, 1588). Some Bruno scholars haveconsidered Bruno's mathesis to be other than simply mathematics. Frances Yatesinterpreted it to be a natural force that lies in between mathematics andphysical things. Hilary Gatti has called it a "meta-mathematics."

My questions is two-fold: 1) how was the term "mathesis" used in the sixteenthcentury; 2) does anyone have any further thoughts as to what it might have meantfor Giordano Bruno.